Geometry / Mr. Hansen 5/2/2008

Name1: _________________________ Name2: _________________________

Nine-Point Circle Project

• Work with a partner.
• Alternate occasionally between who “drives” the computer and who watches.
• Written answers must alternate between partners.
• Illegible or sloppy answers will not be accepted.
• Get help from the online help and/or neighboring groups. Mr. Hansen should be consulted only if you get really stuck.
  
  

1.	Use your segment tool to make . Label the vertices. In the space below, give brief instructions that would tell an incoming Form III student how to do this in the fall. Complete sentences are not required, but clarity is important. Do not proceed to the rest of the project until Mr. Hansen has certified that your instructions are acceptable.
2.	Ask Mr. Hansen for a quick demo of how the selection tool works. This is by far the trickiest part of using Geometer’s Sketchpad.
3.	Construct the midpoint of , and label it as M1. In a similar fashion, construct the midpoints of and , and label them as M2 and M3.
4.	Construct the feet of the altitudes from A, B, and C. Label these feet as F1, F2, and F3, respectively. Make sure that your feet work properly even when the triangle is obtuse. Do not proceed to step 5 until Mr. Hansen has certified that step 4 is correct.
5.	Label the point where the altitudes intersect as “Orthocenter.”
6.	Construct the perpendicular bisectors of all three sides of the triangle by erecting perpendiculars at M1, M2, and M3. Label the intersection of the perpendicular bisectors as “Circumcenter.”
7.	Construct the segment joining the orthocenter and circumcenter, and then construct the midpoint of that segment. Do not label this midpoint.
8.	Using the unlabeled point constructed in step 7, construct a circle centered at that point and with a radius sufficient to make the circle exactly pass through M1, M2, M3, F1, F2, and F3. Obtain Mr. Hansen’s approval before proceeding to step 9.
9.	Construct the midpoints of the three segments that join the orthocenter to the vertices of the triangle. Stretch your triangle around in various ways, and show it to Mr. Hansen. Congratulations!